PL EN


Preferences help
enabled [disable] Abstract
Number of results
Journal
2013 | 11 | 6 | 799-805
Article title

Fractional diffusion equation in half-space with Robin boundary condition

Content
Title variants
Languages of publication
EN
Abstracts
EN
The initial and boundary value problem for the fractional diffusion equation in half-space with the Robin boundary condition is considered. The solution is comprised of two parts: the contribution of the initial value and the contribution of the boundary value, for which the respective fundamental solutions are given. Finally, the solution formula of the considered problem is obtained.
Publisher

Journal
Year
Volume
11
Issue
6
Pages
799-805
Physical description
Dates
published
1 - 6 - 2013
online
9 - 10 - 2013
Contributors
author
  • School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong, 526061, P.R. China
author
  • School of Mathematics and Information Sciences, Zhaoqing University, Zhaoqing, Guang Dong, 526061, P.R. China
References
  • [1] K. B. Oldham, J. Spanier, The Fractional Calculus (Academic, New York, 1974)
  • [2] K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations (Wiley, New York, 1993)
  • [3] F. Mainardi, In: A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics (Springer-Verlag, Wien/New York, 1997) 291
  • [4] I. Podlubny, Fractional Differential Equations (Academic, San Diego, 1999)
  • [5] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006)
  • [6] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity (Imperial College, London, 2010) http://dx.doi.org/10.1142/9781848163300[Crossref]
  • [7] J. Klafter, S. C. Lim, R. Metzler, Fractional Dynamics: Recent Advances (World Scientific, Singapore, 2011) http://dx.doi.org/10.1142/8087[Crossref]
  • [8] D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods (Series on Complexity, Nonlinearity and Chaos) (World Scientific, Boston, 2012)
  • [9] H. Jafari, H. Tajadodi, D. Baleanu, Fract. Calc. Appl. Anal. 16, 109 (2013)
  • [10] D. Baleanu, O. G. Mustafa, D. O’Regan, Adv. Differ. Equ. 2012, 145 (2012) http://dx.doi.org/10.1186/1687-1847-2012-145[Crossref]
  • [11] H. Jafari, A. Kadem, D. Baleanu, T. Yilmaz, Rom. Rep. Phys. 64, 337 (2012)
  • [12] J. S. Duan, T. Chaolu, R. Rach, Appl. Math. Comput. 218, 8370 (2012) http://dx.doi.org/10.1016/j.amc.2012.01.063[Crossref]
  • [13] J. S. Duan, R. Rach, D. Baleanu, A. M. Wazwaz, Commun. Frac. Calc. 3, 73 (2012)
  • [14] J. S. Duan, Z. Wang, Y. L. Liu, X. Qiu, Chaos Soliton. Fract. 46, 46 (2013) http://dx.doi.org/10.1016/j.chaos.2012.11.004[Crossref]
  • [15] M. Giona, H. E. Roman, Physica A 185, 87 (1992) http://dx.doi.org/10.1016/0378-4371(92)90441-R[Crossref]
  • [16] F. Mainardi, Appl. Math. Lett. 9, 23 (1996) http://dx.doi.org/10.1016/0893-9659(96)00089-4[Crossref]
  • [17] F. Mainardi, Chaos Soliton. Fract. 7, 1461 (1996) http://dx.doi.org/10.1016/0960-0779(95)00125-5[Crossref]
  • [18] R. R. Nigmatullin, Phys. Stat. Sol. B 133, 425 (1986) http://dx.doi.org/10.1002/pssb.2221330150[Crossref]
  • [19] R. Metzler, J. Klafter, Physica A 278, 107 (2000) http://dx.doi.org/10.1016/S0378-4371(99)00503-8[Crossref]
  • [20] J. S. Duan, J. Math. Phys. 46, 13504 (2005) http://dx.doi.org/10.1063/1.1819524[Crossref]
  • [21] B. Davies, Integral Transforms and Their Applications, 3rd edition (Springer-Verlag, New York, 2001)
  • [22] R. Gorenflo, J. Loutchko, Y. Luchko, Fract. Calc. Appl. Anal. 5, 491 (2002)
  • [23] J. Abate, P. P. Valkó, Int. J. Numer. Meth. Engng. 60, 979 (2004) http://dx.doi.org/10.1002/nme.995[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_s11534-013-0206-4
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.